MiniMax ε-stable cluster validity index for type-2 fuzziness

Uncertainty is a central part of many data analysis methodologies. Although quantifying the uncertainty has long been discussed, the research on it is still in progress. The level of fuzziness in fuzzy system modeling is a source of uncertainty which can be classified as a parameter uncertainty. Upper and lower values of the level of fuzziness for Fuzzy C-Mean (FCM) clustering methodology have been found as 2.6 and 1.4 respectively in our previous studies. In this paper, we concentrate on the usage of uncertainty associated with the level of fuzziness in determination of the number of clusters in FCM in any data. We propose MiniMax ε-stable cluster validity index based on the uncertainty associated with the level of fuzziness within the framework of Interval Valued Type 2 fuzziness. If the data have a clustered structure, the optimum number of clusters may be assumed to have minimum uncertainty under upper and lower levels of fuzziness. Our investigation shows that the half range of upper and lower levels of fuzziness would be enough to determine the optimum number of clusters.